Document Open Access Logo

Improved Quantum Boosting

Authors Adam Izdebski, Ronald de Wolf

PDF

File

Thumbnail PDF
PDF
LIPIcs.ESA.2023.64.pdf
  • Filesize: 0.7 MB
  • 16 pages

Document Identifiers

Subject Classification

ACM Subject Classification
  • Theory of computation → Quantum computation theory
  • Computing methodologies → Machine learning
Keywords
  • Learning theory
  • Boosting algorithms
  • Quantum computing

Metrics

  • Access Statistics
  • Total Accesses (updated on a weekly basis)
    0
    PDF Downloads
    0
    Metadata Views

Abstract

Boosting is a general method to convert a weak learner (which generates hypotheses that are just slightly better than random) into a strong learner (which generates hypotheses that are much better than random). Recently, Arunachalam and Maity [Srinivasan Arunachalam and Reevu Maity, 2020] gave the first quantum improvement for boosting, by combining Freund and Schapire’s AdaBoost algorithm with a quantum algorithm for approximate counting. Their booster is faster than classical boosting as a function of the VC-dimension of the weak learner’s hypothesis class, but worse as a function of the quality of the weak learner. In this paper we give a substantially faster and simpler quantum boosting algorithm, based on Servedio’s SmoothBoost algorithm [Servedio, 2003].

Cite As Get BibTex

Adam Izdebski and Ronald de Wolf. Improved Quantum Boosting. In 31st Annual European Symposium on Algorithms (ESA 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 274, pp. 64:1-64:16, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2023) https://doi.org/10.4230/LIPIcs.ESA.2023.64

Author Details

Adam Izdebski
  • Faculty of Mathematics, Informatics and Mechanics, University of Warsaw, Poland
Ronald de Wolf
  • QuSoft, CWI and University of Amsterdam, The Netherlands

Funding

  • de Wolf, Ronald: Partially supported by the Dutch Research Council (NWO/OCW), as part of the Quantum Software Consortium programme (project number 024.003.037), and through QuantERA ERA-NET Cofund project QuantAlgo (680-91-034).

Acknowledgements

We thank Srinivasan Arunachalam for many helpful comments, Min-Hsiu Hsieh for sending us an updated version of [Ximing Wang et al., 2021] and answering some questions about this paper, Yassine Hamoudi for answering a question about [Yassine Hamoudi et al., 2020], and the anonymous referees for some helpful pointers.

References

  1. Scott Aaronson and Patrick Rall. Quantum approximate counting, simplified. In Symposium on Simplicity in Algorithms, pages 24-32, 2020. arXiv:1908.10846. Google Scholar
  2. Joran van Apeldoorn and András Gilyén. Improvements in quantum SDP-solving with applications. In Proceedings of 46th ICALP, pages 99:1-99:15, 2019. https://arxiv.org/abs/1804.05058. URL: https://doi.org/10.4230/LIPIcs.ICALP.2019.99.
  3. Joran van Apeldoorn, András Gilyén, Sander Gribling, and Ronald de Wolf. Quantum SDP-solvers: Better upper and lower bounds. Quantum, 4(230), 2020. Earlier version in FOCS'17. URL: https://arxiv.org/abs/1705.01843.
  4. Sanjeev Arora, Elad Hazan, and Satyen Kale. The multiplicative weights update method: a meta-algorithm and applications. Theory of Computing, 8(6):121-164, 2012. URL: https://doi.org/10.4086/toc.2012.v008a006.
  5. Srinivasan Arunachalam and Reevu Maity. Quantum boosting. In Proceedings of 37th International Conference on Machine Learning (ICML'20), pages 377-387, 2020. URL: https://arxiv.org/abs/2002.05056.
  6. Srinivasan Arunachalam and Ronald de Wolf. Guest column: A survey of quantum learning theory. SIGACT News, 48(2):41-67, 2017. URL: https://arxiv.org/abs/1701.06806.
  7. Srinivasan Arunachalam and Ronald de Wolf. Optimal quantum sample complexity of learning algorithms. Journal of Machine Learning Research, 19, 2018. Earlier version in CCC'17. URL: https://arxiv.org/abs/1607.00932.
  8. Boaz Barak, Moritz Hardt, and Satyen Kale. The uniform hardcore lemma via approximate Bregman projections. In Proceedings of 20th ACM-SIAM SODA, pages 1193-1200, 2009. Google Scholar
  9. Jacob Biamonte, Peter Wittek, Nicola Pancotti, P. Rebentrost, Nathan Wiebe, and Seth Lloyd. Quantum machine learning. Nature, 549(7671), 2017. URL: https://arxiv.org/abs/1611.09347.
  10. Fernando G. S. L. Brandão, Amir Kalev, Tongyang Li, Cedric Yen-Yu Lin, Krysta M. Svore, and Xiaodi Wu. Quantum SDP solvers: Large speed-ups, optimality, and applications to quantum learning. In Proceedings of 46th ICALP, pages 27:1-27:14, 2019. https://arxiv.org/abs/1710.02581. URL: https://doi.org/10.4230/LIPIcs.ICALP.2019.27.
  11. Fernando G. S. L. Brandão and Krysta M. Svore. Quantum speed-ups for solving semidefinite programs. In Proceedings of 58th IEEE FOCS, pages 415-426, 2017. https://arxiv.org/abs/1609.05537. URL: https://doi.org/10.1109/FOCS.2017.45.
  12. Gilles Brassard, Peter Høyer, Michele Mosca, and Alain Tapp. Quantum amplitude amplification and estimation. In Quantum Computation and Quantum Information: A Millennium Volume, volume 305 of AMS Contemporary Mathematics Series, pages 53-74. AMS, 2002. URL: https://arxiv.org/abs/quant-ph/0005055.
  13. Yoav Freund and Robert E. Schapire. A decision-theoretic generalization of on-line learning and an application to boosting. Journal of Computer and System Sciences, 5:119-139, 1997. Google Scholar
  14. Yoav Freund, Robert E. Schapire, and Naoki Abe. A short introduction to boosting. Journal of the Japanese Society For Artificial Intelligence, 14(771-780):1612, 1999. Google Scholar
  15. Lov K. Grover. A fast quantum mechanical algorithm for database search. In Proceedings of 28th ACM STOC, pages 212-219, 1996. quant-ph/9605043. Google Scholar
  16. Yassine Hamoudi, Maharshi Ray, Patrick Rebentrost, Miklos Santha, Xin Wang, and Siyi Yang. Quantum algorithms for hedging and the Sparsitron. https://arxiv.org/abs/2002.06003, 2020.
  17. Phil M. Long and Rocco A. Servedio. Learning large-margin halfspaces with more malicious noise. In Proceedings of NIPS, pages 91-99, 2011. Google Scholar
  18. Patrick Rebentrost, Yassine Hamoudi, Maharshi Ray, Xin Wang, Siyi Yang, and Miklos Santha. Quantum algorithms for hedging and the learning of ising models. Phys. Rev. A, 103:012418, January 2021. URL: https://doi.org/10.1103/PhysRevA.103.012418.
  19. Robert E. Schapire and Yoav Freund. Boosting: Foundations and algorithms. Kybernetes, 2013. Google Scholar
  20. Robert E. Schapire, Yoav Freund, Peter Bartlett, and Wee Sun Lee. Boosting the margin: a new explanation for the effectiveness of voting methods. In Proceedings of 14th International Conference on Machine Learning (ICML'97), pages 322-330, 1997. Google Scholar
  21. Maria Schuld and Francesco Petruccione. Quantum ensembles of quantum classifiers. Scientific reports, 8(1):1-12, 2018. URL: https://arxiv.org/abs/1704.02146.
  22. Rocco A. Servedio. Smooth boosting and learning with malicious noise. Journal of Machine Learning Research, 4:633-648, 2003. Earlier version in COLT/EuroCOLT'01. Google Scholar
  23. Shai Shalev-Shwartz and Shai Ben-David. Understanding Machine Learning - From Theory to Algorithms. Cambridge University Press, 2014. Google Scholar
  24. Ximing Wang, Yuechi Ma, Min-Hsiu Hsieh, and Manhong Yung. Quantum speedup in adaptive boosting of binary classification. Science China Physics, Mechanics & Astronomy, 64(2):220311, 2021. URL: https://arxiv.org/abs/1902.00869.
Questions / Remarks / Feedback
X

Feedback for Dagstuhl Publishing


Thanks for your feedback!

Feedback submitted

Could not send message

Please try again later or send an E-mail
© 2023-2025 Schloss Dagstuhl – LZI GmbH About DROPS Imprint Privacy Contact